This metric quantifies this importance in terms of optimal disruptive events classified following the Granovetter's theory for single-layer networks [1]}: the importance of a node in preserving a network's giant component depends on the connectivity of the node. In particular, nodes which shares weak connections tend to be those more important to be preserved. Heel-ness measures the importance of a node considering the weakest connection it has, and the number of unreachable nodes after that edge disruption.
The Granovetter's theory was proposed in 1973 in the context of social networks. Since then it was studied and proposed in countless different fields of application. Following a similar approach we adapt the measures introduced in [2]} to detect important ties in transport networks. In particular we focus our attention on the topological resilience of multilayer networks as proposed in [3]}. Topological resilience studies the robustness of a network in resisting to topological failures, such as edge removal. Heel-ness measures the single-event effects of the network and ranks them depending on the greatest damage they can inflict to the network structure if one particular edge is removed. Extending then the idea from [1]} to transport networks allows us to refer to weak ties as those edges that make the network more fragile and susceptible to targeted edge loss. We stress further that topological resilience takes into account only the network structure while edges can be weighted in such a way that more important links, e.g. in a transport network those links that sustain higher traffic flows, are naturally considered as more crucial for the overall system connectivity.
